Question

find the solutions to the system of nonlinear equations given by:
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$$\begin{cases} y = 4x + 1 \\\\ y = -x^2 + 1 \\end{cases}$$

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a:
b:
use the graph to determine which point is a and b.
enter your answer as an ordered pair. for example: \\((2, -5)\\)

Explanation:

Step1: Equate the two equations

$$4x + 1 = -x^2 + 1$$

Step2: Simplify the equation

$$x^2 + 4x = 0$$

Step3: Solve for x

$$x(x + 4) = 0 \implies x = 0 \text{ or } x = -4$$

Step4: Find corresponding y-values

$$x = 0 \implies y = 1$$

$$x = -4 \implies y = -15$$

Step5: Identify points from graph

$$A = (0, 1)$$

$$B = (-4, -15)$$

Answer:

A: \((0, 1)\)
B: \((-4, -15)\)